Nonzero-sum Discrete-time Stochastic Games with Risk-sensitive Ergodic Cost Criterion
Optimization and Control
2024-08-26 v1 Probability
Abstract
In this paper we study infinite horizon nonzero-sum stochastic games for controlled discrete-time Markov chains on a Polish state space with risk-sensitive ergodic cost criterion. Under suitable assumptions we show that the associated ergodic optimality equations admit unique solutions. Finally, the existence of Nash-equilibrium in randomized stationary strategies is established by showing that an appropriate set-valued map has a fixed point.
Keywords
Cite
@article{arxiv.2408.12849,
title = {Nonzero-sum Discrete-time Stochastic Games with Risk-sensitive Ergodic Cost Criterion},
author = {Bivakar Bose and Chandan Pal and Somnath Pradhan and Subhamay Saha},
journal= {arXiv preprint arXiv:2408.12849},
year = {2024}
}